Photon momentum sharing between an electron and an ion in photoionization: from one-photon (photoelectric effect) to multiphoton absorption

Role of the Binding Energy on Nondipole Effects in Single-Photon Ionization

We experimentally study the influence of the binding energy on nondipole effects in K-shell single-photon ionization of atoms at high photon energies. We find that for each ionization event, as expected by momentum conservation, the photon momentum is transferred almost fully to the recoiling ion. The momentum distribution of the electrons becomes asymmetrically deformed along the photon propagation direction with a mean value of 8/(5c)(E_{γ}-I_{P}) confirming an almost 100 year old prediction by Sommerfeld and Schur [Ann. Phys. (N.Y.) 396, 409 (1930)10.1002/andp.19303960402]. The emission direction of the photoions results from competition between the forward-directed photon momentum and the backward-directed recoil imparted by the photoelectron. Which of the two counteracting effects prevails depends on the binding energy of the emitted electron. As an example, we show that at 20 keV photon energy, Ne^{+} and Ar^{+} photoions are pushed backward towards the radiation source, while Kr^{+} photoions are emitted forward along the light propagation direction.

Floquet Engineering to Overcome No-Go Theorem of Noisy Quantum Metrology

Permitting a more precise measurement to physical quantities than the classical limit by using quantum resources, quantum metrology holds a promise in developing many revolutionary technologies. However, the noise-induced decoherence forces its superiority to disappear, which is called no-go theorem of noisy quantum metrology and constrains its application. We propose a scheme to overcome the no-go theorem by Floquet engineering. It is found that, by applying a periodic driving on the atoms of the Ramsey spectroscopy, the ultimate sensitivity to measure their frequency characterized by quantum Fisher information returns to the ideal t^{2} scaling with the encoding time whenever a Floquet bound state is formed by the system consisting of each driven atom and its local noise. Combining with the optimal control, this mechanism also allows us to retrieve the ideal Heisenberg-limit scaling with the atom number N. Our result gives an efficient way to avoid the no-go theorem of noisy quantum metrology and to realize high-precision measurements.

Double-Slit Interference in the Ion Dynamics of Dissociative Photoionization

The ion momentum distribution in the x-ray-induced dissociative photoionization of molecules is investigated, treating the ionization analytically under the Born-Oppenheimer approximation and simulating numerically the ion motion via the Schrödinger equation. The ion-photoelectron entanglement transfers information of the electronic interference to the ion dynamics. As a consequence, the ion momentum distributions of dissociative molecular photoionization present Young's double-slit interference when the photoelectron emission angle is fixed. We demonstrate that double-slit interference signatures persist in the ion longitudinal momentum shift even when the information of the correlated photoelectron is lost, which is the case for heteronuclear molecules when an additional photoelectron recoil momentum arises due to the different ion masses. For the case of sequential double ionization, we show that double-slit interference in the ion dynamics can be utilized for coherent control of the molecular dynamics.

Quasifree Photoionization under the Reaction Microscope

We experimentally investigated the quasifree mechanism (QFM) in one-photon double ionization of He and H2 at 800 eV photon energy and circular polarization with a COLTRIMS reaction microscope. Our work provides new insight into this elusive photoionization mechanism that was predicted by Miron Amusia more than four decades ago. We found the distinct four-fold symmetry in the angular emission pattern of QFM electrons from H2 double ionization that has previously only been observed for He. Furthermore, we provide experimental evidence that the photon momentum is not imparted onto the center of mass in quasifree photoionization, which is in contrast to the situation in single ionization and in double ionization mediated by the shake-off and knock-out mechanisms. This finding is substantiated by numerical results obtained by solving the system’s full-dimensional time-dependent Schrödinger equation beyond the dipole approximation.

Nondipole Time Delay and Double-Slit Interference in Tunneling Ionization

Recently two-center interference in single-photon molecular ionization was employed to observe a zeptosecond time delay due to the photon propagation of the internuclear distance in a molecule [Grundmann et al., Science 370, 339 (2020)SCIEAS0036-807510.1126/science.abb9318]. We investigate the possibility of a comparable nondipole time delay in tunneling ionization and decode the emerged time delay signal. With the here newly developed Coulomb-corrected nondipole molecular strong-field approximation, we derive and analyze the photoelectron momentum distribution, the signature of nondipole effects, and the role of the degeneracy of the molecular orbitals. We show that the ejected electron momentum shifts and interference fringes efficiently imprint both the molecule structure and laser parameters. The corresponding nondipole time delay value significantly deviates from that in single-photon ionization. In particular, when the two-center interference in the molecule is destructive, the time delay is independent of the bond length. We also identify the double-slit interference in tunneling ionization of atoms with nonzero angular momentum via a nondipole momentum shift.

Photoelectron energy peaks shift against the radiation pressure in strong-field ionization

The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules, the photoelectron energy does not depend on the electron's emission direction, but theoretical studies have questioned this since 1990. Here, we provide experimental evidence that the energies of photoelectrons emitted against the light propagation direction are shifted toward higher values, while those electrons that are emitted along the light propagation direction are shifted to lower values. We attribute the energy shift to a nondipole contribution to the ponderomotive potential that is due to the interaction of the moving electrons with the incident photons.

Magnetic-Field Effect as a Tool to Investigate Electron Correlation in Strong-Field Ionization

The influence of the magnetic component of the driving electromagnetic field is often neglected when investigating light-matter interaction. We show that the magnetic component of the light field plays an important role in nonsequential double ionization, which serves as a powerful tool to investigate electron correlation. We investigate the magnetic-field effects in double ionization of xenon atoms driven by near-infrared ultrashort femtosecond laser pulses and find that the mean forward shift of the electron momentum distribution in light-propagation direction agrees well with the classical prediction, where no under-barrier or recollisional nondipole enhancement is observed. By extending classical trajectory Monte Carlo simulations beyond the dipole approximation, we reveal that double ionization proceeds via recollision-induced doubly excited states, followed by subsequent sequential over-barrier field ionization of the two electrons. In agreement with this model, the binding energies do not lead to an additional nondipole forward shift of the electrons. Our findings provide a new method to study electron correlation by exploiting the effect of the magnetic component of the electromagnetic field.

Magnetic-Field Effect in High-Order Above-Threshold Ionization

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the 2U_{p} classical cutoff is found to be vastly different from that below this cutoff, where U_{p} is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

Distribution of absorbed photons in the tunneling ionization process

We describe a procedure that allows us to solve the three-dimensional time-dependent Schrödinger equation for an atom interacting with a quantized one-mode electromagnetic field. Atom-field interaction is treated in an ab initio way prescribed by quantum electrodynamics. We use the procedure to calculate probability distributions of absorbed photons in the regime of tunneling ionization. We analyze evolution of the reduced photon density matrix describing the state of the field. We show that non-diagonal density matrix elements decay quickly, as a result of the decoherence process. A stochastic model, viewing ionization as a Markovian birth-death process, reproduces the main features of the calculated photon distributions.

Electric Nondipole Effect in Strong-Field Ionization

Strong-field ionization of atoms by circularly polarized femtosecond laser pulses produces a donut-shaped electron momentum distribution. Within the dipole approximation this distribution is symmetric with respect to the polarization plane. The magnetic component of the light field is known to shift this distribution forward. Here, we show that this magnetic nondipole effect is not the only nondipole effect in strong-field ionization. We find that an electric nondipole effect arises that is due to the position dependence of the electric field and which can be understood in analogy to the Doppler effect. This electric nondipole effect manifests as an increase of the radius of the donut-shaped photoelectron momentum distribution for forward-directed momenta and as a decrease of this radius for backwards-directed electrons. We present experimental data showing this fingerprint of the electric nondipole effect and compare our findings with a classical model and quantum calculations.

Theory of Subcycle Linear Momentum Transfer in Strong-Field Tunneling Ionization

Interaction of a strong laser pulse with matter transfers not only energy but also linear momentum of the photons. Recent experimental advances have made it possible to detect the small amount of linear momentum delivered to the photoelectrons in strong-field ionization of atoms. We present numerical simulations as well as an analytical description of the subcycle phase (or time) resolved momentum transfer to an atom accessible by an attoclock protocol. We show that the light-field-induced momentum transfer is remarkably sensitive to properties of the ultrashort laser pulse such as its carrier-envelope phase and ellipticity. Moreover, we show that the subcycle-resolved linear momentum transfer can provide novel insights into the interplay between nonadiabatic and nondipole effects in strong-field ionization. This work paves the way towards the investigation of the so-far unexplored time-resolved nondipole nonadiabatic tunneling dynamics.

Observation of Photoion Backward Emission in Photoionization of He and N_{2}

We experimentally investigate the effects of the linear photon momentum on the momentum distributions of photoions and photoelectrons generated in one-photon ionization in an energy range of 300  eV≤E_{γ}≤40  keV. Our results show that for each ionization event the photon momentum is imparted onto the photoion, which is essentially the system's center of mass. Nevertheless, the mean value of the ion momentum distribution along the light propagation direction is backward-directed by -3/5 times the photon momentum. These results experimentally confirm a 90-year-old prediction.

Dissecting Strong-Field Excitation Dynamics with Atomic-Momentum Spectroscopy

Observation of internal quantum dynamics relies on correlations between the system being observed and the measurement apparatus. We propose using the c.m. degrees of freedom of atoms and molecules as a "built-in" monitoring device for observing their internal dynamics in nonperturbative laser fields. We illustrate the idea on the simplest model system-the hydrogen atom in an intense, tightly focused infrared laser beam. To this end, we develop a numerically tractable, quantum-mechanical treatment of correlations between internal and c.m. dynamics. We show that the transverse momentum records the time excited states experience the field, allowing femtosecond reconstruction of the strong-field excitation process. The ground state becomes weak-field seeking, an unambiguous and long sought-for signature of the Kramers-Henneberger regime.

Photon Momentum Transfer in Single-Photon Double Ionization of Helium

We theoretically and experimentally investigate the photon momentum transfer in single-photon double ionization of helium at various large photon energies. We find that the forward shifts of the momenta along the light propagation of the two photoelectrons are roughly proportional to their fraction of the excess energy. The mean value of the forward momentum is about 8/5 of the electron energy divided by the speed of light. This holds for fast and slow electrons despite the fact that the energy sharing is highly asymmetric and the slow electron is known to be ejected by secondary processes of shake off and knockout rather than directly taking its energy from the photon. The biggest deviations from this rule are found for the region of equal energy sharing where the quasifree mechanism dominates double ionization.

Attosecond-Scale Streaking Methods for Strong-Field Ionization by Tailored Fields

Streaking with a weak probe field is applied to ionization in a two-dimensional strong field tailored to mimic linear polarization, but without disturbance by recollision or intracycle interference. This facilitates the observation of electron-momentum-resolved times of ionization with few-attosecond precision, as demonstrated by simulations for a model helium atom. Aligning the probe field along the ionizing field provides meaningful ionization times in agreement with the attoclock concept that ionization at maximum field corresponds to the peak of the momentum distribution, which is shifted due to the Coulomb force on the outgoing electron. In contrast, this attoclock shift is invisible in orthogonal streaking. Even without a probe field, streaking happens naturally along the laser propagation direction due to the laser magnetic field. As with an orthogonal probe field, the attoclock shift is not accessible by the magnetic-field scheme. For a polar molecule, the attoclock shift depends on orientation, but this does not imply an orientation dependence in ionization time.

Sub-cycle time resolution of multi-photon momentum transfer in strong-field ionization

During multi-photon ionization of an atom it is well understood how the involved photons transfer their energy to the ion and the photoelectron. However, the transfer of the photon linear momentum is still not fully understood. Here, we present a time-resolved measurement of linear momentum transfer along the laser pulse propagation direction. We can show that the linear momentum transfer to the photoelectron depends on the ionization time within the laser cycle using the attoclock technique. We can mostly explain the measured linear momentum transfer within a classical model for a free electron in a laser field. However, corrections are required due to the parent-ion interaction and due to the initial momentum when the electron enters the continuum. The parent-ion interaction induces a negative attosecond time delay between the appearance in the continuum of the electron with minimal linear momentum transfer and the point in time with maximum ionization rate.

Photoelectron Holographic Interferometry to Probe the Longitudinal Momentum Offset at the Tunnel Exit

Laser-induced electron tunneling underlies numerous emerging spectroscopic techniques to probe attosecond electron dynamics in atoms and molecules. The improvement of those techniques requires an accurate knowledge of the exit momentum for the tunneling wave packet. Here we demonstrate a photoelectron interferometric scheme to probe the electron momentum longitudinal to the tunnel direction at the tunnel exit by measuring the photoelectron holographic pattern in an orthogonally polarized two-color laser pulse. In this scheme, we use a perturbative 400-nm laser field to modulate the photoelectron holographic fringes generated by a strong 800-nm pulse. The fringe shift offers direct experimental access to the intermediate canonical momentum of the rescattering electron, allowing us to reconstruct the momentum offset at the tunnel exit with high accuracy. Our result unambiguously proves the existence of nonzero initial longitudinal momentum at the tunnel exit and provides fundamental insights into the nonquasistatic nature of the strong-field tunneling.

Strong Field Theories beyond Dipole Approximations in Nonrelativistic Regimes

The exact nondipole Volkov solutions to the Schrödinger equation and Pauli equation are found, based on which a strong field theory beyond the dipole approximation is built for describing the nondipole effects in nonrelativistic laser driven electron dynamics. This theory is applied to investigate momentum partition laws for multiphoton and tunneling ionization and explicitly shows that the complex interplay of a laser field and Coulomb action may reverse the expected photoelectron momentum along the laser propagation direction. The magnetic-spin coupling does not bring observable effects on the photoelectron momentum distribution and can be neglected. Compared to the strong field approximation within the dipole approximation, this theory works in a much wider range of laser parameters and lays a solid foundation for describing nonrelativistic electron dynamics in both short wavelength and midinfrared regimes where nondipole effects are unavoidable.